Abstract
The link between Obesity and Hypertension is among the most popular topics which have been explored in medical research in recent decades. However, it is challenging to establish the relationship comprehensively and accurately because the distribution of BMI and blood pressure is usually fat tailed and severely tied. In this paper, we propose a data-driven copulas selection approach via penalized likelihood which can deal with tied data by interval censoring estimation. Minimax Concave Penalty is involved to perform the unbiased selection of mixed copula model for its convergence property to get un-penalized solution. Interval censoring and maximizing pseudo-likelihood, inspired from survival analysis, is introduced by considering ranks as intervals with upper and lower limits. This paper describes the model and corresponding iterative algorithm. Simulations to compare the proposed approach versus existing methods in different scenarios are presented. Additionally, the proposed method is also applied to the association modeling on the China Health and Nutrition Survey (CHNS) data. Both numerical studies and real data analysis reveal good performance of the proposed method.
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Acknowledgement
Dr. Y Li is supported by Platform of Public Health & Disease Control and Prevention, Major Innovation & Planning Interdisciplinary Platform for the “Double-First Class” Initiative, Renmin University of China and the National Scientific Foundation of China (71771211).
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Appendices
Appendix
See Tables 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.
1 Supported tables for simulation design
2 Line plots of correctness rates
Figures 3 and 4 are based on results from Table 2 and Table 3, respectively. In below figures, the proposed method is mentioned as ‘Proposed’ due to limited space.
3 Estimated results (\(n=500\)) of MSE and Bias
4 Simulated results of sample size \(n=200\)
5 Supportive simulations
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Li, Y., Wang, F., Shen, Y. et al. Selection of mixed copula for association modeling with tied observations. Stat Methods Appl 31, 1127–1180 (2022). https://doi.org/10.1007/s10260-022-00628-3
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DOI: https://doi.org/10.1007/s10260-022-00628-3